Finite Group Databasebeta

← C61×#61838 #29565271

Subgroups — C61×#61838 #29565271

Order 15616.

1700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3523C211yesmaximal, characteristic
2C2×Q82×C61C211yesmaximal, characteristic, complemented
3C61×#3387C216yesmaximal, complemented
4Q8×SD16×C61C212yesmaximal, complemented
5C61×#3369C216yesmaximal, complemented
6C61×#3363C212yesmaximal, complemented
7C61×#3238C213yesmaximal
8C61×#3229C213yesmaximal, complemented
9C61×#3113C213yesmaximal, complemented
10C61×#3108C213yesmaximal
11C61×#2984C211yesmaximal, characteristic, complemented
12Q82×C61—23no—
13Q82×C61—21no—
14Q82×C61C2212yes—
15Q82×C61C2216yes—
16C61×#557C2211yescharacteristic
17C61×#557C2213yes—
18C61×#556C2213yes—
19C61×#552—23no—
20D4×Q8×C61—21no—
21D4×Q8×C61C2211yescharacteristic
22C61×#541—23no—
23C61×#533C2213yes—
24C2×C4⋊Q8×C61—23no—
25C2×C4⋊Q8×C61C2213yes—
26C61×#529C2213yes—
27C61×#519—21no—
28C2×C4×Q8×C61—21no—
29C2×C4×Q8×C61C2213yes—
30C2×C4×Q8×C61C2211yescharacteristic
31C61×#501C2216yes—
32C61×#498C2216yes—
33C61×#489C2216yes—
34C61×#487C2216yes—
35C61×#483C2213yes—
36C61×#483C2216yes—
37C61×#480C2213yes—
38C61×#479C2216yes—
39C61×#477C2216yes—
40C61×#476C2216yes—
41C61×#475C2216yes—
42C61×#475C22112yes—
43C61×#464C2216yes—
44C61×#462C2216yes—
45C61×#451C2213yes—
46C61×#448C2211yescharacteristic
47C61×#446C2216yes—
48C8×Q8×C61C2212yes—
49C61×#441C22112yes—
50C4×Q16×C61C2216yes—
51C4×SD16×C61C2216yes—
52C61×#432C2213yes—
53C61×#431C2213yes—
54C22×Q8×C61—21no—
55C22×Q8×C61—23no—
56C22×Q8×C61D411yescharacteristic
57C22×Q8×C61C2311yescharacteristic
58C2×Q16×C61C2316yes—
59C2×SD16×C61C2312yes—
60C4⋊Q8×C61—23no—
61C4⋊Q8×C61—26no—
62C4⋊Q8×C61—26no—
63C4⋊Q8×C61—212no—
64C4⋊Q8×C61—23no—
65C4⋊Q8×C61—23no—
66C4⋊Q8×C61C2313yes—
67C4⋊Q8×C61C2316yes—
68C4⋊Q8×C61C2316yes—
69C4⋊Q8×C61C2313yes—
70#126×C61—26no—
71#126×C61—23no—
72#125×C61—26no—
73#125×C61—23no—
74#125×C61—23no—
75#125×C61C2313yes—
76#124×C61C2313yes—
77#123×C61—23no—
78C22⋊Q8×C61—23no—
79C22⋊Q8×C61—23no—
80C22⋊Q8×C61—23no—
81C22⋊Q8×C61C2313yes—
82#121×C61C2311yescharacteristic
83C4×Q8×C61—21no—
84C4×Q8×C61—26no—
85C4×Q8×C61—22no—
86C4×Q8×C61—23no—
87C4×Q8×C61—23no—
88C4×Q8×C61—23no—
89C4×Q8×C61—23no—
90C4×Q8×C61D413yes—
91C4×Q8×C61D411yescharacteristic
92C4×Q8×C61C2316yes—
93C4×Q8×C61C2313yes—
94C4×Q8×C61C2316yes—
95C4×Q8×C61C2316yes—
96C4×Q8×C61C2311yescharacteristic
97C4×Q8×C61C2313yes—
98C4×D4×C61—23no—
99C4×D4×C61C2313yes—
100#117×C61—23no—
101#117×C61—23no—
102#117×C61—23no—
103C2×C4⋊C4×C61—23no—
104C2×C4⋊C4×C61—23no—
105C2×C4⋊C4×C61D413yes—
106C2×C4⋊C4×C61C2313yes—
107C2×C42×C61—23no—
108C2×C42×C61C2313yes—
109#107×C61C2316yes—
110#106×C61C2316yes—
111#106×C61C23112yes—
112C4⋊C8×C61C2316yes—
113C4⋊C8×C61C2316yes—
114#103×C61C2316yes—
115#103×C61C2312yes—
116#103×C61C2316yes—
117#103×C61C23112yes—
118#102×C61C2316yes—
119C22⋊C8×C61C2311yescharacteristic
120C22⋊C8×C61C2313yes—
121#97×C61C2316yes—
122C4×C8×C61C2316yes—
123C2×Q8×C61—24no—
124C2×Q8×C61—24no—
125C2×Q8×C61—21no—
126C2×Q8×C61—23no—
127C2×Q8×C61—26no—
128C2×Q8×C61—26no—
129C2×Q8×C61—44no—
130C2×Q8×C61—86no—
131C2×Q8×C61C2×D413yes—
132C2×Q8×C61C2×D411yescharacteristic
133C2×Q8×C61C2413yes—
134C2×Q8×C61C2412yes—
135C2×D4×C61—21no—
136C2×D4×C61C2411yescharacteristic
137C22×C4×C61—21no—
138C22×C4×C61—23no—
139C22×C4×C61—23no—
140C22×C4×C61C2×D413yes—
141C22×C4×C61C2×D413yes—
142C22×C4×C61C2411yescharacteristic
143Q16×C61—212no—
144SD16×C61—24no—
145C2×C8×C61C2412yes—
146C2×C8×C61C2416yes—
147C4⋊C4×C61—26no—
148C4⋊C4×C61—26no—
149C4⋊C4×C61—26no—
150C4⋊C4×C61—26no—
151C4⋊C4×C61—23no—
152C4⋊C4×C61—23no—
153C4⋊C4×C61—23no—
154C4⋊C4×C61—23no—
155C4⋊C4×C61—23no—
156C4⋊C4×C61—23no—
157C4⋊C4×C61—23no—
158C4⋊C4×C61—26no—
159C4⋊C4×C61—23no—
160C4⋊C4×C61C2×D413yes—
161C4⋊C4×C61C2×D413yes—
162C4⋊C4×C61C2×D416yes—
163C4⋊C4×C61C2416yes—
164C4⋊C4×C61C2413yes—
165C4⋊C4×C61C2411yescharacteristic
166C22⋊C4×C61—23no—
167C22⋊C4×C61—21no—
168C22⋊C4×C61—23no—
169C22⋊C4×C61—23no—
170C22⋊C4×C61—23no—
171C42×C61—26no—
172C42×C61—26no—
173C42×C61—26no—
174C42×C61—23no—
175C42×C61C2×D413yes—
176C42×C61C2×D413yes—
177C42×C61C2413yes—
178C42×C61C2413yes—
179C23×C61—21no—
180C23×C61C22×D411yescharacteristic
181Q8×C61—24no—
182Q8×C61—26no—
183Q8×C61—22no—
184Q8×C61—26no—
185Q8×C61—46no—
186Q8×C61—86no—
187Q8×C61—86no—
188Q8×C61#13714yes—
189Q8×C612−1+414yes—
190D4×C61—22no—
191D4×C61—42no—
192C2×C4×C61—24no—
193C2×C4×C61—26no—
194C2×C4×C61—22no—
195C2×C4×C61—26no—
196C2×C4×C61—22no—
197C2×C4×C61—23no—
198C2×C4×C61—21no—
199C2×C4×C61—23no—
200C2×C4×C61—26no—
201C2×C4×C61—46no—
202C2×C4×C61—46no—
203C2×C4×C61C22×D413yes—
204C2×C4×C61C22×D413yes—
205C2×C4×C61C22×D411yescharacteristic
206C2×C4×C61C22×D413yes—
207C2×C4×C61C22×D413yes—
208C2×C4×C61C2511yescharacteristic
209C8×C61—22no—
210C8×C61—26no—
211#61838C6111yesmaximal, characteristic, direct product factor, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61#57712yes—
218C22×C61C23×D411yescharacteristic
219C4×C61—24no—
220C4×C61—21no—
221C4×C61—23no—
222C4×C61—23no—
223C4×C61—23no—
224C4×C61—43no—
225C4×C61—43no—
226C4×C61—46no—
227C4×C61—41no—
228C4×C61C2×#13716yes—
229C4×C61C2×2−1+412yes—
230#3523C2×C6111yescharacteristic
231C2×Q82C2×C6111yescharacteristic, complemented
232#3387C2×C6116yescomplemented
233Q8×SD16C2×C6112yescomplemented
234#3369C2×C6116yescomplemented
235#3363C2×C6112yescomplemented
236#3238C2×C6113yes—
237#3229C2×C6113yescomplemented
238#3113C2×C6113yescomplemented
239#3108C2×C6113yes—
240#2984C2×C6111yescharacteristic, complemented
241C2×C61—22no—
242C2×C61—81no—
243C2×C61#348611yescharacteristic
244C2×C61C22×#13711yescharacteristic
245C2×C61C2×#57711yescharacteristic
246Q82—21no—
247Q82—23no—
248Q82C22×C6112yes—
249Q82C22×C6116yes—
250#557C22×C6111yescharacteristic
251#557C22×C6113yes—
252#556C22×C6113yes—
253#552—23no—
254D4×Q8—21no—
255D4×Q8C22×C6111yescharacteristic
256#541—23no—
257#533C22×C6113yes—
258C2×C4⋊Q8—23no—
259C2×C4⋊Q8C22×C6113yes—
260#529C22×C6113yes—
261#519—21no—
262C2×C4×Q8—21no—
263C2×C4×Q8C22×C6113yes—
264C2×C4×Q8C22×C6111yescharacteristic
265#501C22×C6116yes—
266#498C22×C6116yes—
267#489C22×C6116yes—
268#487C22×C6116yes—
269#483C22×C6113yes—
270#483C22×C6116yes—
271#480C22×C6113yes—
272#479C22×C6116yes—
273#477C22×C6116yes—
274#476C22×C6116yes—
275#475C22×C6116yes—
276#475C22×C61112yes—
277#464C22×C6116yes—
278#462C22×C6116yes—
279#451C22×C6113yes—
280#448C22×C6111yescharacteristic
281#446C22×C6116yes—
282C8×Q8C22×C6112yes—
283#441C22×C61112yes—
284C4×Q16C22×C6116yes—
285C4×SD16C22×C6116yes—
286#432C22×C6113yes—
287#431C22×C6113yes—
288C61#6183811yescharacteristic, direct product factor, Sylow
289C22×Q8—21no—
290C22×Q8—23no—
291C22×Q8D4×C6111yescharacteristic
292C22×Q8C23×C6111yescharacteristic
293C2×Q16C23×C6116yes—
294C2×SD16C23×C6112yes—
295C4⋊Q8—23no—
296C4⋊Q8—26no—
297C4⋊Q8—26no—
298C4⋊Q8—212no—
299C4⋊Q8—23no—
300C4⋊Q8—23no—
301C4⋊Q8C23×C6113yes—
302C4⋊Q8C23×C6116yes—
303C4⋊Q8C23×C6116yes—
304C4⋊Q8C23×C6113yes—
305#126—26no—
306#126—23no—
307#125—26no—
308#125—23no—
309#125—23no—
310#125C23×C6113yes—
311#124C23×C6113yes—
312#123—23no—
313C22⋊Q8—23no—
314C22⋊Q8—23no—
315C22⋊Q8—23no—
316C22⋊Q8C23×C6113yes—
317#121C23×C6111yescharacteristic
318C4×Q8—26no—
319C4×Q8—22no—
320C4×Q8—21no—
321C4×Q8—23no—
322C4×Q8—23no—
323C4×Q8—23no—
324C4×Q8—23no—
325C4×Q8D4×C6111yescharacteristic
326C4×Q8D4×C6113yes—
327C4×Q8C23×C6116yes—
328C4×Q8C23×C6116yes—
329C4×Q8C23×C6113yes—
330C4×Q8C23×C6116yes—
331C4×Q8C23×C6111yescharacteristic
332C4×Q8C23×C6113yes—
333C4×D4—23no—
334C4×D4C23×C6113yes—
335#117—23no—
336#117—23no—
337#117—23no—
338C2×C4⋊C4—23no—
339C2×C4⋊C4—23no—
340C2×C4⋊C4D4×C6113yes—
341C2×C4⋊C4C23×C6113yes—
342C2×C42—23no—
343C2×C42C23×C6113yes—
344#107C23×C6116yes—
345#106C23×C6116yes—
346#106C23×C61112yes—
347C4⋊C8C23×C6116yes—
348C4⋊C8C23×C6116yes—
349#103C23×C6116yes—
350#103C23×C6112yes—
351#103C23×C6116yes—
352#103C23×C61112yes—
353#102C23×C6116yes—
354C22⋊C8C23×C6111yescharacteristic
355C22⋊C8C23×C6113yes—
356#97C23×C6116yes—
357C4×C8C23×C6116yes—
358C2×Q8—24no—
359C2×Q8—24no—
360C2×Q8—21no—
361C2×Q8—23no—
362C2×Q8—26no—
363C2×Q8—26no—
364C2×Q8—44no—
365C2×Q8—86no—
366C2×Q8C2×D4×C6113yes—
367C2×Q8C2×D4×C6111yescharacteristic
368C2×Q8C24×C6113yes—
369C2×Q8C24×C6112yes—
370C2×D4—21no—
371C2×D4C24×C6111yescharacteristic
372C22×C4—21no—
373C22×C4—23no—
374C22×C4—23no—
375C22×C4C2×D4×C6113yes—
376C22×C4C2×D4×C6113yes—
377C22×C4C24×C6111yescharacteristic
378Q16—212no—
379SD16—24no—
380C2×C8C24×C6112yes—
381C2×C8C24×C6116yes—
382C4⋊C4—26no—
383C4⋊C4—26no—
384C4⋊C4—26no—
385C4⋊C4—26no—
386C4⋊C4—23no—
387C4⋊C4—23no—
388C4⋊C4—23no—
389C4⋊C4—23no—
390C4⋊C4—23no—
391C4⋊C4—23no—
392C4⋊C4—23no—
393C4⋊C4—26no—
394C4⋊C4—23no—
395C4⋊C4C2×D4×C6113yes—
396C4⋊C4C2×D4×C6113yes—
397C4⋊C4C2×D4×C6116yes—
398C4⋊C4C24×C6116yes—
399C4⋊C4C24×C6113yes—
400C4⋊C4C24×C6111yescharacteristic
401C22⋊C4—23no—
402C22⋊C4—21no—
403C22⋊C4—23no—
404C22⋊C4—23no—
405C22⋊C4—23no—
406C42—26no—
407C42—26no—
408C42—26no—
409C42—23no—
410C42C2×D4×C6113yes—
411C42C2×D4×C6113yes—
412C42C24×C6113yes—
413C42C24×C6113yes—
414C23—21no—
415C23C22×D4×C6111yescharacteristic
416Q8—24no—
417Q8—26no—
418Q8—22no—
419Q8—26no—
420Q8—46no—
421Q8—86no—
422Q8—86no—
423Q8#137×C6114yes—
424Q82−1+4×C6114yes—
425D4—22no—
426D4—42no—
427C2×C4—24no—
428C2×C4—26no—
429C2×C4—22no—
430C2×C4—26no—
431C2×C4—22no—
432C2×C4—23no—
433C2×C4—21no—
434C2×C4—23no—
435C2×C4—26no—
436C2×C4—46no—
437C2×C4—46no—
438C2×C4C22×D4×C6113yes—
439C2×C4C22×D4×C6113yes—
440C2×C4C22×D4×C6111yescharacteristic
441C2×C4C22×D4×C6113yes—
442C2×C4C22×D4×C6113yes—
443C2×C4C25×C6111yescharacteristic
444C8—22no—
445C8—26no—
446C22—21no—
447C22—21no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22C61×#57712yes—
452C22C23×D4×C6111yescharacteristic
453C4—23no—
454C4—23no—
455C4—23no—
456C4—24no—
457C4—21no—
458C4—43no—
459C4—46no—
460C4—41no—
461C4—43no—
462C4C2×#137×C6116yes—
463C4C2×2−1+4×C6112yes—
464C2—22no—
465C2—81no—
466C2C61×#348611yescharacteristic
467C2C22×#137×C6111yescharacteristic
468C2C2×C61×#57711yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radical#121×C61C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×Q82×C61C2semidirect
3. C61×#3387C2semidirect
4. Q8×SD16×C61C2semidirect
5. C61×#3369C2semidirect
6. C61×#3363C2semidirect
8. C61×#3229C2semidirect
9. C61×#3113C2semidirect
11. C61×#2984C2semidirect
211. #61838C61direct (N × H)
231. C2×Q82C2×C61semidirect
232. #3387C2×C61semidirect
233. Q8×SD16C2×C61semidirect
234. #3369C2×C61semidirect
235. #3363C2×C61semidirect
237. #3229C2×C61semidirect
238. #3113C2×C61semidirect
240. #2984C2×C61semidirect
288. C61#61838direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C61×#35232
C2×Q82×C612
C61×#33872
Q8×SD16×C612
C61×#33692
C61×#33632
C61×#32382
C61×#32292
C61×#31132
C61×#31082
C61×#29842
#6183861